Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12749 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#578 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
882 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,29,25,21,23,28)(20,30,34,46,35,47,33,44)(22,37,40,36,41,45,39,27)(26,38,43,49,31,48,42,32);(18,20)(19,26)(21,31)(22,38)(23,33)(24,34)(25,35)(27,44)(28,42)(29,43)(30,37)(32,39)(36,46)(40,49)(41,48)(45,47);(15,17)(18,21,25,19)(20,31,35,26)(22,36,41,27)(23,28,24,29)(30,32,47,49)(33,42,34,43)(37,39,45,40)(38,46,48,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5737);